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Multicellular Computing: Dynamic Complexity

When dynamic elements in a system adapt to other dynamic elements, they generate positive feedback loops. Qualitatively different and often surprising new phenomena emerge as a result.

Unexpected behavior emerges by the continued action of positive feedback in adaptive complex systems. Consider an example of positive feedback that is familiar to most of us: a microphone induces a loud squeal from a speaker when the microphone gets too close to the speaker or the amplifier gain is turned up too high. The positive feedback occurs because the sound picked up from the microphone is amplified, sent out through the speaker and returns to the microphone to be picked up louder than before. Once you understand the mechanism, it seems unremarkable and controllable. To kill the squeal, simply move the microphone farther from the speaker or turn down the amplifier gain.

Similar, though less manageable, positive feedback tends to emerge in random networks. As a thought experiment, consider a large open space, say a football field, on which a hundred speakers, amplifiers and microphones are placed randomly. Now, begin adding connections (wires), one at a time, between a randomly chosen microphone and amplifier or randomly chosen amplifier and speaker[1]. Sooner or later, a squeal will arise because a speaker happens to be close enough to the microphone that feeds it. Let us call that trio an autocatalytic set, i.e., a self-reinforcing set of elements that produce an emergent property of the system (the squeal). Adding more wires will soon create a second squeal, and a third, and so on. There tends to be a threshold beyond which new feedback loops are created very rapidly and shortly thereafter nearly all the speakers will be emitting squeals. Because the output of any given speaker reaches more than one microphone, some of the autocatalytic sets (i.e., feedback loops) may involve more than one microphone/amplifier/speaker trio. Likewise, a given speaker or microphone may be participating in more than one autocatalytic set, i.e., emitting multiple squeals at various pitches (because the pitch depends upon the distance between the participating speaker and microphone).

In 1965, Stuart Kauffman did a more formal experiment analogous to the speakers on the football field using random Boolean nets in a computer simulation. It showed, to his surprise, that autocatalytic sets (called state cycles in these Boolean nets) inevitably emerge very quickly and the number of autocatalytic sets that will emerge is roughly the square root of the number of elements in the Boolean network [2]. More generally, mutually reinforcing feedback loops form in all sorts of complex systems. The probability of the emergence of autocatalytic sets increases as more elements are added, more interconnections are added, or the elements themselves become more complex and therefore can interact with others in more complex ways. In other words, any change to the system that increases the number of possible feedback loops increases the probability of an autocatalytic set, hence an emergent phenomenon.

Familiar natural examples include:

Sand dunes -- Dunes form from the simple interactions of very large numbers of grains of sand with each other and with the wind. If there is enough sand being blown by the wind, any obstruction can start the formation of a dune. A bush, a fence post or even an ant hill may be sufficient. If the pile of sand is large and steep enough to create a “wind shadow,” more sand will collect in the shadow, enlarging the pile. Given a sufficient supply of sand and wind, the emerging sand dune may eventually grow to more than 300 meters in height and move as much as 20 meters per year. In North China and the Sahara, sand dunes threaten to engulf entire towns.

Money -- Coins, in the form of chunks of metal or cowrie shells, emerged as early as 5000 BC. But money became really useful once coins with specific values, i.e., denominations, emerged about 700BC in Lydia (now a part of Turkey). Before were minted, commerce was done by barter which limited commercial exchanges to pairs of people who desired what the other had (or perhaps three-way exchanges that were very difficult to arrange). Coins allowed a new kind of commercial interaction between people, one in which the money provided an agreed upon temporary store of value that was neither specific to a particular commodity or service, nor to a specific place and time. Feedback arose because, as the benefits of using money were made clear, more coins were minted which allowed those benefits to be experienced by more and more traders. Within two hundred years, the idea of using coins with specific denominations had spread throughout the Medeteranian region and all the way to China. Commerce was changed forever.

The Internet -- In computing, TCP/IP and HTTP protocols create new sorts of interactions between computers. The Internet emerged from TCP/IP and the Web emerged from HTTP. P2P protocols are another example. They supported the emergence of Napster and its descendents such as BitTorrent that now threaten to obsolete the music recording industry. These sorts of systems grow because of the positive feedback of what is known as the “network effect.” That is, as the network grows it becomes more attractive for others to join the network. Telephones and fax machines are the usual example of prototypical positive feedback network effects.

Complex dynamic feedback gives rise to an emergent entity that is qualitatively different from that of its elements. Sand dunes are far different from grains of sand, both in scale and in behavior. A marketplace based upon money rather than barter is qualitatively different because easily communicable prices emerge that create relationships between all goods and services. More specialized goods and services can participate on an equal footing with everyday commodities. And, the emergent behavior called the Web is dramatically different from communities that swap files by FTP even though the technical differences between FTP and HTTP are relatively minor.

How big does a system have to be before feedback loops become nearly inevitable? It tuns out that it depends upon how complex their interactions are -- the simpler the elements and their interactions, the more of them are needed to give a high probability of emergence.

[1] Note: since this is an abstract thought experiment, we allow multiple microphones to feed the same amplifier, a microphone to feed multiple amplifiers, and an amplifier to feed multiple speakers. We also ignore the likelihood that, in real life, amplifiers may blow fuses and speakers may shred themselves.